A probabilistically Checkable Proof (PCP) allows a randomized
verifier, with oracle access to a purported proof, to
probabilistically verify

an input statement of the form ``$x\in L$'' by querying only few bits
of the proof. A \emph{PCP of proximity} (PCPP) has the additional
feature of allowing the verifier to query only few bits of the {\em
input} $x$, where if the input is accepted then the verifier is
guaranteed that (with high probability) the input is \emph{close} to
some $x'\in L$.

Motivated by their usefulness for sublinear-communication
cryptography, we initiate the study of a natural zero-knowledge
variant of PCPP (ZKPCPP), where the view of any verifier making a
bounded number of queries can be efficiently simulated by making the
same number of queries to \emph{the input oracle alone}. This new
notion provides a useful extension of the standard notion of
zero-knowledge PCPs. We obtain two types of results.

Constructions. We obtain the first constructions of
query-efficient ZKPCPPs via a general transformation which combines
standard query-efficient PCPPs with protocols for secure multiparty
computation. As a byproduct, our construction provides a conceptually
simpler alternative to a previous construction of honest-verifier
zero-knowledge PCPs due to Dwork et al. (Crypto '92).

Applications. We motivate the notion of ZKPCPPs by applying
it towards sublinear-communication implementations of commit-and-prove
functionalities. Concretely, we present the first
sublinear-communication commit-and-prove protocols which make a {\em
black-box} use of a collision-resistant hash function, and the first
such multiparty protocols which offer {\em information-theoretic}
security in the presence of an honest majority.